10x-1=2/1x-3

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Solution for 10x-1=2/1x-3 equation:



10x-1=2/1x-3
We move all terms to the left:
10x-1-(2/1x-3)=0
Domain of the equation: 1x-3)!=0
x∈R
We get rid of parentheses
10x-2/1x+3-1=0
We multiply all the terms by the denominator
10x*1x+3*1x-1*1x-2=0
Wy multiply elements
10x^2+3x-1x-2=0
We add all the numbers together, and all the variables
10x^2+2x-2=0
a = 10; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·10·(-2)
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*10}=\frac{-2-2\sqrt{21}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*10}=\frac{-2+2\sqrt{21}}{20} $

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